Abstract

Different materials with different phase changes on reflection affect the surface-height measurement when interferometric techniques are employed for testing objects constructed of different materials that are adjacent to one another. We test the influence of this phase change on reflection when vertical scanning interferometry with a broadband source is used. We show theoretically and experimentally that the strong linear dependence of the dispersion of the phase change on reflection preserves the shape of the coherence envelope of the fringes but shifts it along the optical axis by approximately 10–40 nm for metallic surfaces.

© 2001 Optical Society of America

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References

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  1. J. C. Wyant, J. Schmit, “Computerized interferometric measurement of surface microstructure,” in Optical Inspection and Micromeasurements, C. Gorecki, ed., Proc. SPIE2782, 26–37 (1996).
    [CrossRef]
  2. M. Born, E. Wolf, in Principles of Optics, 6th ed. (Pergamon, New York, 1980), p. 60.
  3. J. F. Biegen, “Determination of the phase change on reflection from two-beam interference,” Opt. Lett. 19, 1690–1692 (1994).
    [CrossRef] [PubMed]
  4. E. D. Palik, in Handbook of Optical Constants of Solids, E. D. Palik, ed. (Academic, New York, 1985), pp. 275–804.
  5. S. Suja Helen, M. P. Kothiyal, R. S. Sirohi, “Phase shifting by a rotating polarizer in white-light interferometry for surface profiling,” J. Mod. Opt. 46, 993–1001 (1999).
  6. K. G. Larkin, “Effective nonlinear algorithm for envelope detection in white light interferometry,” J. Opt. Am. A 13, 832–843 (1996).
    [CrossRef]
  7. P. Sandoz, R. Devillers, A. Plata, “Unambiguous profilometry by fringe-order identification in white-light phase-shifting interferometry,” J. Mod. Opt. 44, 519–534 (1997).
    [CrossRef]
  8. A. Harasaki, J. Schmit, J. C. Wyant, “Improved vertical scanning interferometry,” Appl. Opt. 39, 2107–2115 (2000).
    [CrossRef]
  9. C. Ai, E. L. Novak, “Centroid approach for estimating modulation peak in broad-bandwidth interferometry,” U.S. patent5,633,715 (27May1997, filed 19May1996).

2000 (1)

1999 (1)

S. Suja Helen, M. P. Kothiyal, R. S. Sirohi, “Phase shifting by a rotating polarizer in white-light interferometry for surface profiling,” J. Mod. Opt. 46, 993–1001 (1999).

1997 (1)

P. Sandoz, R. Devillers, A. Plata, “Unambiguous profilometry by fringe-order identification in white-light phase-shifting interferometry,” J. Mod. Opt. 44, 519–534 (1997).
[CrossRef]

1996 (1)

K. G. Larkin, “Effective nonlinear algorithm for envelope detection in white light interferometry,” J. Opt. Am. A 13, 832–843 (1996).
[CrossRef]

1994 (1)

Ai, C.

C. Ai, E. L. Novak, “Centroid approach for estimating modulation peak in broad-bandwidth interferometry,” U.S. patent5,633,715 (27May1997, filed 19May1996).

Biegen, J. F.

Born, M.

M. Born, E. Wolf, in Principles of Optics, 6th ed. (Pergamon, New York, 1980), p. 60.

Devillers, R.

P. Sandoz, R. Devillers, A. Plata, “Unambiguous profilometry by fringe-order identification in white-light phase-shifting interferometry,” J. Mod. Opt. 44, 519–534 (1997).
[CrossRef]

Harasaki, A.

Kothiyal, M. P.

S. Suja Helen, M. P. Kothiyal, R. S. Sirohi, “Phase shifting by a rotating polarizer in white-light interferometry for surface profiling,” J. Mod. Opt. 46, 993–1001 (1999).

Larkin, K. G.

K. G. Larkin, “Effective nonlinear algorithm for envelope detection in white light interferometry,” J. Opt. Am. A 13, 832–843 (1996).
[CrossRef]

Novak, E. L.

C. Ai, E. L. Novak, “Centroid approach for estimating modulation peak in broad-bandwidth interferometry,” U.S. patent5,633,715 (27May1997, filed 19May1996).

Palik, E. D.

E. D. Palik, in Handbook of Optical Constants of Solids, E. D. Palik, ed. (Academic, New York, 1985), pp. 275–804.

Plata, A.

P. Sandoz, R. Devillers, A. Plata, “Unambiguous profilometry by fringe-order identification in white-light phase-shifting interferometry,” J. Mod. Opt. 44, 519–534 (1997).
[CrossRef]

Sandoz, P.

P. Sandoz, R. Devillers, A. Plata, “Unambiguous profilometry by fringe-order identification in white-light phase-shifting interferometry,” J. Mod. Opt. 44, 519–534 (1997).
[CrossRef]

Schmit, J.

A. Harasaki, J. Schmit, J. C. Wyant, “Improved vertical scanning interferometry,” Appl. Opt. 39, 2107–2115 (2000).
[CrossRef]

J. C. Wyant, J. Schmit, “Computerized interferometric measurement of surface microstructure,” in Optical Inspection and Micromeasurements, C. Gorecki, ed., Proc. SPIE2782, 26–37 (1996).
[CrossRef]

Sirohi, R. S.

S. Suja Helen, M. P. Kothiyal, R. S. Sirohi, “Phase shifting by a rotating polarizer in white-light interferometry for surface profiling,” J. Mod. Opt. 46, 993–1001 (1999).

Suja Helen, S.

S. Suja Helen, M. P. Kothiyal, R. S. Sirohi, “Phase shifting by a rotating polarizer in white-light interferometry for surface profiling,” J. Mod. Opt. 46, 993–1001 (1999).

Wolf, E.

M. Born, E. Wolf, in Principles of Optics, 6th ed. (Pergamon, New York, 1980), p. 60.

Wyant, J. C.

A. Harasaki, J. Schmit, J. C. Wyant, “Improved vertical scanning interferometry,” Appl. Opt. 39, 2107–2115 (2000).
[CrossRef]

J. C. Wyant, J. Schmit, “Computerized interferometric measurement of surface microstructure,” in Optical Inspection and Micromeasurements, C. Gorecki, ed., Proc. SPIE2782, 26–37 (1996).
[CrossRef]

Appl. Opt. (1)

J. Mod. Opt. (2)

S. Suja Helen, M. P. Kothiyal, R. S. Sirohi, “Phase shifting by a rotating polarizer in white-light interferometry for surface profiling,” J. Mod. Opt. 46, 993–1001 (1999).

P. Sandoz, R. Devillers, A. Plata, “Unambiguous profilometry by fringe-order identification in white-light phase-shifting interferometry,” J. Mod. Opt. 44, 519–534 (1997).
[CrossRef]

J. Opt. Am. A (1)

K. G. Larkin, “Effective nonlinear algorithm for envelope detection in white light interferometry,” J. Opt. Am. A 13, 832–843 (1996).
[CrossRef]

Opt. Lett. (1)

Other (4)

E. D. Palik, in Handbook of Optical Constants of Solids, E. D. Palik, ed. (Academic, New York, 1985), pp. 275–804.

J. C. Wyant, J. Schmit, “Computerized interferometric measurement of surface microstructure,” in Optical Inspection and Micromeasurements, C. Gorecki, ed., Proc. SPIE2782, 26–37 (1996).
[CrossRef]

M. Born, E. Wolf, in Principles of Optics, 6th ed. (Pergamon, New York, 1980), p. 60.

C. Ai, E. L. Novak, “Centroid approach for estimating modulation peak in broad-bandwidth interferometry,” U.S. patent5,633,715 (27May1997, filed 19May1996).

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Figures (3)

Fig. 1
Fig. 1

Phase change on reflection of metals4 as a function of wave number.

Fig. 2
Fig. 2

Phase change on reflection of semiconductors4 as a function of wave number.

Fig. 3
Fig. 3

Simulated correlograms, sampled every 80 nm as is typical in real measurement, from silver and glass surfaces. (a) From silver side, (b) from glass side. The offset is estimated to be 36 nm by use of the centroid approach.9

Tables (1)

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Table 1 Height Offsets Comparison of VSI and PSI Techniques

Equations (14)

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ϕ0ν=arctan2κν1-κ2ν-n2ν,
ϕ0ν=a0+a1ν+a2ν2+a3ν3+.
Mz  ν1ν2cos2πν2z+ϕ0νdν,
Mz  ν1ν2cos2πν2z+a0+a1ν+a2ν2+a3ν3+dν=ν1ν2cos2πν2z+a12π+a0+a2ν2+a3ν3+dν=Reν1ν2exp-i2πν2z+a12π+a0×exp-ia2ν2+a3ν3+dν.
a2ν2+a3ν3+a0+a1ν  2π
exp-ia2ν2+a3ν3+=1-ia2ν2-ia3ν3-.
Mz  Reν1ν2exp-i2πν2z+a12π+a0×1-ia2ν2-ia3ν3-dν=Reν1ν2exp-i2πν2z+a12π+a0dν-Reia2ν1ν2ν2 exp-i2πν2z+a12π+a0dν-Reia3ν1ν2ν3 exp-i2πν2z+a12π+a0dν
-.
ν¯ν1+ν22,
Δνν2-ν1.
Mz  Re(exp-ia0×exp-i2πν¯ξΔν sincΔνξ|ξ=2z+a1/2π)+Reexp-ia0ia2-i2π2×d2d2ξexp-i2πν¯ξΔν×sincΔνξ|ξ=2z+a1/2π+Reexp-ia0ia3-i2π3×d3d3ξexp-i2πν¯ξΔν sincΔνξ|ξ=2z+a1/2π+
Mz  Δν cos2πν¯ξ+a0sincΔνξ|ξ=2z+a1/2π+a2ν¯2Δν sin2πν¯ξ+a0sincΔνξ|ξ=2z+a1/2π+a3ν¯3Δν sin2πν¯ξ+a0sincΔνξ|ξ=2z+a1/2π+=Δν sincΔνξcos2πν¯ξ+a0+a2ν¯2+a3ν¯3+sin2πν¯ξ+a0|ξ=2z+a1/2π.
Mz  Δν sincΔνξcos2πν¯ξ+a0+α|ξ=2z+a1/2π,
α=arctana2ν¯2+a3ν¯3+a2ν¯2+a3ν¯3+.

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